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The Sign Test, Paired Data, and Asymmetric Dependence: A Cautionary Tale
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| Pengarang | : | Alan D. Hutson |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 35-40 |
| Abstrak | : | In the paired data setting, the sign test is often described in statistical textbooks as a test for comparing differences between the medians of two marginal distributions. There is an implicit assumption that the median of the differences is equivalent to the difference of the medians when employing the sign test in this fashion. We demonstrate however that given asymmetry in the bivariate distribution of the paired data, there are often scenarios where the median of the differences is not equal to the difference of the medians. Further, we show that these scenarios will lead to a false interpretation of the sign test for its intended use in the paired data setting. We illustrate the false-interpretation concept via theory, a simulation study, and through a real-world example based on breast cancer RNA sequencing data obtained from the Cancer Genome Atlas (TCGA). |
Analytical expressions for stability regions in the Ince–Strutt diagram of Mathieu equation
| Pengarang | : | Eugene I. Butikov |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 4) |
| Halaman | : | 257-267 |
| Abstrak | : | Simple analytical expressions are suggested for transition curves that separate, in the Ince–Strutt diagram, different types of solutions to the famous Mathieu equation. The derivations of these expressions in this paper rely on physically meaningful periodic solutions describing various regular motions of a familiar nonlinear mechanical system—a rigid planar pendulum with a vertically oscillating pivot. The paper is accompanied by a relevant simulation program. |
Sinking bubbles in stout beers
| Pengarang | : | W. T. Lee |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 4) |
| Halaman | : | 250-256 |
| Abstrak | : | A surprising phenomenon witnessed by many is the sinking bubbles seen in a settling pint of stout beer. Bubbles are less dense than the surrounding fluid so how does this happen? Previous work has shown that the explanation lies in a circulation of fluid promoted by the tilted sides of the glass. However, this work has relied heavily on computational fluid dynamics (CFD) simulations. Here, we show that the phenomenon of sinking bubbles can be predicted using a simple analytic model. To make the model analytically tractable, we work in the limit of small bubbles and consider a simplified geometry. The model confirms both the existence of sinking bubbles and the previously proposed mechanism. |
On Arbitrarily Underdispersed Discrete Distributions
| Pengarang | : | Alan Huang |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 29-34 |
| Abstrak | : | We survey a range of popular generalized count distributions, investigating which (if any) can be arbitrarily underdispersed, that is, its variance can be arbitrarily small compared to its mean. A philosophical implication is that some models failing this simple criterion should not be considered as “statistical models” according to McCullagh’s extendibility criterion. Four practical implications are also discussed: (i) functional independence of parameters, (ii) double generalized linear models, (iii) simulation of underdispersed counts, and (iv) severely underdispersed count regression. We suggest that all future generalizations of the Poisson distribution be tested against this key property. |
Fresnel's original interpretation of complex numbers in 19th century optics
| Pengarang | : | Ricardo Karam |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 4) |
| Halaman | : | 245-249 |
| Abstrak | : | In 1823, Fresnel published an original (physical) interpretation of complex numbers in his investigations of refraction and reflection of polarized light. This is arguably the first time that complex numbers were given a physical interpretation, which led to a better understanding of elliptical and circular polarizations. This rather unknown episode of the history of physics is described in this work, and some of the pedagogical lessons that can be extracted from it are discussed. |
Coherent Tests for Interval Null Hypotheses
| Pengarang | : | Spencer Hansen |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 20-28 |
| Abstrak | : | In a celebrated 1996 article, Schervish showed that, for testing interval null hypotheses, tests typically viewed as optimal can be logically incoherent. Specifically, one may fail to reject a specific interval null, but nevertheless—testing at the same level with the same data—reject a larger null, in which the original one is nested. This result has been used to argue against the widespread practice of viewing p-values as measures of evidence. In the current work we approach tests of interval nulls using simple Bayesian decision theory, and establish straightforward conditions that ensure coherence in Schervish’s sense. From these, we go on to establish novel frequentist criteria—different to Type I error rate—that, when controlled at fixed levels, give tests that are coherent in Schervish’s sense. The results suggest that exploring frequentist properties beyond the familiar Neyman–Pearson framework may ameliorate some of statistical testing’s well-known problems. |
A Study on the Power Parameter in Power Prior Bayesian Analysis
| Pengarang | : | Zifei Han |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 12-19 |
| Abstrak | : | The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power δ. The derivation of the marginal likelihood based on the original power prior, and its variation, the normalized power prior, introduces a scaling factor ?????(????) in the form of a prior predictive distribution with powered likelihood. In this article, we show that the scaling factor might be infinite for some positive δ with conventionally used initial priors, which would change the admissible set of the power parameter. This result seems to have been almost completely ignored in the literature. We then illustrate that such a phenomenon may jeopardize the posterior inference under the power priors when the initial prior of the model parameters is improper. The main findings of this article suggest that special attention should be paid when the suggested level of borrowing is close to 0, while the actual optimum might be below the suggested value. We use a normal linear model as an example for illustrative purposes. |
Bayesian Testing of Linear Versus Nonlinear Effects Using Gaussian Process Priors
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 1-11 |
| Abstrak | : | A Bayes factor is proposed for testing whether the effect of a key predictor variable on a dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) in substantive research for assessing the nature of the relationship between certain variables based on scientific expectations, and (ii) for statistical model building to infer whether a (transformed) variable should be added as a linear or nonlinear predictor in a regression model. Under the nonlinear model, a Gaussian process prior is employed using a parameterization similar to Zellner’s g prior resulting in a scale-invariant test. Unlike existing p-values, the proposed Bayes factor can be used for quantifying the relative evidence in the data in favor of linearity. Furthermore the Bayes factor does not overestimate the evidence against the linear null model resulting in more parsimonious models. An extension is proposed for Bayesian one-sided testing of whether a nonlinear effect is consistently positive, consistently negative, or neither. Applications are provided from various fields including social network research and education. |
ERNST BLOCH: SEORANG ATEIS-MARXIS PEMBUKA JALAN TEOLOGI HARAPAN
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Fenomena |
| Volume / Edisi | : | 1/3, OKTOBER-DESEMBER (No. 1) |
| Halaman | : | 64-69 |
| Abstrak | : | Harapan merupakan salah satu daya dorong manusia untuk bertahan hidup atau untuk menata hidup di masa depan. Dengan adanya harapan, manusia didorong untuk hidup dalam keadaan dinamis. Namun demikian tidak setiap orang menyadari dan mencoba memahami harapan secara intelektual. Ernst Bloch seorang ateis Marxis mencoba menggulatinya. Pergulatan tersebut tidak terlepas dari perjalanan pemikiran pendahulunya. Pemikirannya ternyata juga memberikan sumbangan pada teolog-teolog kristen dalam merefleksikan hidup imannya. Dengan harapan, iman tidaklah sia-sia. |
ATEISME: SEBUAH TANTANGAN KEBERIMANAN
| Pengarang | : | Sumargo Petrus Simon |
| Nama Majalah/Jurnal | : | Fenomena |
| Volume / Edisi | : | 1/3, OKTOBER-DESEMBER (No. 1) |
| Halaman | : | 60-63 |
| Abstrak | : | Dalam uraiannya, Sumarga mencoba mencari hal-hal mengapa manusia dapat mengabaikan Realitas Absolut, atau dengan kata lain yang lebih populer: Tuhan. Ternyata memang ada hal-hal menarik menyangkut uraiannya. Salah satunya, ternyata sejarah mengatakan bahwa yang ditolak oleh para penganut ateis itu sebenarnya 'gagasan Tuhan' yang diciptakan oleh manusia.Tuhan yang mentransformasi dunia, Tuhan yang menekan kebebasan manusia, dan lain-lain. Tentu saja karena Tuhan 'de facto' tidak bisa dialami oleh manusia secara penuh selama ia masih hidup di dunia, jadi yang mereka lawan adalah Tuhan 'de iure' yang gagasannya diciptakan oleh manusia. Sebentar lagi kita akan mengikuti secara sekilas bagaimana pemikiran ateis berdialog dengan pemikiran para teis berkisar masalah Tuhan. Suatu dialog yang banyak dipengaruhi oleh struktur budaya-sosial-pemikiran filosofis pada masa itu. |